Time series are data observed over time (either in continuous time or at discrete time periods).

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Definition of Time Series

Time series model is defined as : A time series model specifies the joint distribution of the sequence ${\{X_t}\}$ of random variables. For example:$$P[X_1\le x_1,\ldots,X_t\le x_t]$$ for all $t$ and ...
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root mean square error in forecasting

I have to use ARIMA model to forecast real prices of aluminium and copper in eviews. I have to do in sample and out of sample forecasting. my data set is annual from 1960 till 2014. I have selected a ...
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Suggested algorithms for time series analysis of sporadic events

I have a series of sporadic, discrete time series events that appear to occur in shorter interval clusters and I am looking for a way to determine the frequencies at which the events occur. None of ...
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The sample variance is an inefficient estimator of the conditional variance in a t-GARCH model?

Harvey states in this paper (2008) at the end of the second page that: "The possible inappropriateness of letting $\sigma^2_{t|t-1}$ be a linear function of past squared observations when $v$ is ...
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Differencing a series and back

I've followed this procedure: I have a non-stationary process (call it 'series_1'), which I try to render stationary by differencing. The largest value of the process (8760 observations) is about ...
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determinstic trend in VAR-models

I'm asking myself the following question. I want to build a VAR-Model with 6 time series A, B, C, D, E and F. I analysed every series univariate and I found out that A, D, E and F are stationary and B ...
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Conditional entropy and Spearman's correlation based lag in time series

I have two time series A, B. Both are seasonal and B primarily is A driven( other temporal causes may exist). B-Red, A- Green I want to calculate lag of red series with respect to green as clearly, ...
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Is the the dependence of the residual of a ARMA time series model only based on AR term?

Lets suppose we fit two time series models AR(1) and ARMA(1,1) to a data series. Should be the results of the ljung-Box test for the residuals be the same for these models? I mean does MA term affect ...
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Relation between raw and central moments

This question arose when reading Johansen's likelihood-based inference in cointegrated VAR models, the 2009 reprint, page 146. I will do my best to make my post self-contained. Let $Z_{0t}=\Delta ...
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Estimate linear regression paramaters with chain modeling for longitudinal data?

Within a frequentist, deterministic paradigm of multiple linear regression, is there a (standard) method to accomplish "chain modeling for panel data" in a way that avoids formal identity (and/or ...
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time series based classification

I want to classify some data. Basically the data is time series in nature. The target variable is categorical. I know there are so many algorithms for predicting the time series model. However, I have ...
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Regression with autocorrelated, lagged independent variable

Dear Cross Validated Community I have a question about handling dependencies in time-series regression. This is not an urgent issue. However, it would be nice to have a little discussion here - if ...
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How to align two seasonal time series

I am trying to decompose a time series using Holt Winters method and use it for forecast. I am trying to do this for weekly data of last 25-26 months. The challenge is that the dates of the seasonal ...
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How to adjust rank for ad for its recent trend in click-through-rate?

I am building an optimization service for an Adtech company. For ranking ads in terms of performance, I am using formula: Log(impressions)*eCPM. Impressions means the number of times ad was ...
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Question about intervention analysis in time series

I have two questions: First, I fit a seasonal ARIMA model to a time series before a certain event and get the residuals diagnostics below: And the AICc is 16.35399, the smallest among the seasonal ...
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On a parametrization of an infinite series to recover the GARCH process

Time series analysis By James D. Hamilton (a great book) proceeds in this way to introduce the GARCH process: First it recalls that the equation that described an ARCH(m) process was the following: ...
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General Regression Equation for Time Series data

Could someone explain me in laymen terms for the difference between General Regression Equation and General Time Series Regression equation? Below, is the question. Also, why is epsilon present in an ...
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What is the logic behind using Adstock VS VAR style lag analysis for marketing mix models?

I'd like to discern why the adstock transformation is the default method to introduce lagged influence of prior time points i marketing mix models over a standard linear method as in VAR? I understand ...
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Classifying the Next Call

Suppose I have calls that come from handsets A, B, C, and time series data aggregated like so: ...
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ADF test results confusion

When I ran ADF test with my data set, I got following results. I am confused about why "alternative hypothesis" is always (even for real non-stationary series) showing as "stationary"? ...
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Doubt in state space representation for time series model

$y$ is scalar observations and so C will be a 1x2 matrix. I want to represent the following model as a state space representation so as to estimate the hidden states from the noisy observations $y$ ...
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Testing for covariance on a fixed scale?

I'm struggling on finding a way to analyse my data, that may be fixed just with a basic statistics insight. I have a dataset that has a large number of variables (100+) some of which tend to covary ...
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How to scale a Hanning Window so that the sum of its squared weights equals the length of the time series?

I am trying to implement the following method described here: http://www.geo.uni-bremen.de/geomod/staff/mschulz/reprint/spectrum.pdf At the 4th page, in the paragraph above the 4th equation, I have ...
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Difference between static and dynamic linear regression

A static linear regression has the form $y_t = \mathbf{x}_t'\boldsymbol{\theta} + \epsilon_t$ while a dynamic linear regression has the form $y_t = \mathbf{x}_t'\boldsymbol{\theta}_t + \epsilon_t$. ...
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Difference between random walk and process integrated of order one?

I know that an $I(1)$ process becomes stationary after differencing once. However, I somehow always equated that to its being a random walk because say having a unit root process like \begin{eqnarray} ...
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What normalization factor to use in Inverse Discrete Fourier Transform of Cross-Spectrum?

I have applied the Lomb-Scargle approach to estimating the cross-spectrum of two irregularly sampled time series and I am trying to obtain their cross-correlation by applying the inverse Discrete ...
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Methods for determining cause and effect relationships between time lagged variables?

As you know, one can use regression for inference to learn which variables correlate with a response variable if the input predictors and the response share the same time frame. Let's say a predictor ...
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Recommendations for fitting a classifier on panel data to predict one step head forecasted class

I am predicting the binary class, i.e. if it's in top10 or not, of a security based upon it's performance using predictors from current time. So it's simply a cross sectional classifier. As of now ...
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Sampling of a real time-correlated random variable

I would like to sample numerically the real-value time-continuous random variable $X(t)$, which verifies: $$E[X(t)X(s)]=f(t-s).$$ In my case, $f$ is given by $$f(t)=\frac{1-t^2}{1+t^2}.$$ -My first ...
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Granger causality result interpretation in R

I am unable to interpret what this means.T2 is a zoo object containing two two price series. MSBVAR library of ...
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Interpreting tbats seasonal results for looking for the type of seasonality

Using tbatsfunction in R to look for seasonality. I test the seasonality for weekly and every 10 days and both have seasonality. ...
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138 views

Predicting the growth of traffic on a web site: regression or time series?

I've got a small website and I'm investing a lot of efforts on it. The traffic is growing but still very low. I've studied engineering but my knowledge of statistics is basic. I have put the last 70 ...
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Neural network for time series forecasting- Single input Single output Theoretical proof needed

I am doing time series forecasting using neural networks. I have 2 approaches: Forecasting in a auto regressive manner i.e based on time series lags as shown below: ...
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Creating regular time series from irregular time series (with data changes only)

I am using data from a sensor, that only sends the value if it has changed with the timestamp of the data change. The result looks for example like this: ...
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ACF values in identifying non-stationarity

I have used NIST data to calculate ACF in excel which worked fine and coded in our programming language (NOT R). Here is the plot of ACF: Now my questions are: 1) From this ACF series how can I ...
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R seasonal time series

I use the decompose function in R and come up with the 3 components of my monthly time series (trend, seasonal and random). If I ...
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ANOVA on unevenly spaced time data

I have a dataset with three treatments (P+, P- and T) and want to test the effect of the treatment on the mortality (continuous variable). Data are unevenly spaced in time. I decided to handel this by ...
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Interaction in Multiple Regression with Lagged Variable

The problem I'm trying to solve is as follows: X is a strong predictor of Y, both measured at time T, controlling for other IVs. Based on theory, some people say this supports the hypothesis that X ...
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Looking for Pattern in Daily Data in Time Series

I have a sample data here for a daily time series and I want to how can I find out if it shows a weekly or 10 day pattern. ...
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Constructing a data set for visualization

I am enrolled in a data analysis course and part of a course, I need to find a time series data set and generate visualizations and predictions based on my understanding of the findings. Instead of ...
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How is Gram-Schmidt procedure used in the following time series context?

I was reading the innovation algorithm in Brickel's Time Series Theory and Methods (page 171-172). Let $H$ denotes a Hilbert space, $P$ denotes the projection operator and $\bar{sp}$ denotes closed ...
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On the prediction mean square error of a model

Suppose my model is $y_t = \alpha + \beta t + \epsilon_t$ the l-step-ahead prediction is given by $\hat{y}_{T+l | T} = a + b(T + l)$ where $a$ and $b$ are the OLS estimators of $\alpha$ and $\beta$. ...
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For time series classification, how can k nearest neighbors outperform other models?

Suppose you have a collections of time series data $Y^1,\ldots,Y^N$, $Y^i = Y^i_1,\ldots,Y^i_T$. Your training data consists of labels for some of these $Y^i$, and you wish to infer labels for the ...
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Estimation of fractional order of integration in ARFIMA model

I wish to model monthly EUR/USD exchange rate by an ARFIMA($p,d,q$) model. My question is, how to determine the $d$ parameter of this model?
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Should I aggregate my panel data into a single time series for interrupted time series analysis?

I have a very large dataset containing individuals observed daily on some variable Y. I would like to find out whether some event X that occurred simultaneously to all individuals (a global event) ...
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Interpretation of ARIMA with xreg in R

I've fitted a model with auto arima, with independent variables with the below codes: ...
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What do you think is the right tooling to separate sub-time series from a single big time series?

I would like to separate a big time series into its components to improve forecasting. To clarify: I would like to find the different components - maybe it is better to say frequencies which ...
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Can I use correlation metrics also for time series?

I was using the cross correlation function in R (ccf) until now to discover correlations and lags between two time series. I was wondering if I can use all other ...
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Testing differences in slope in time series of repeated measures data

I have a dataset wherein we measured a response in each sample at 20 time points for 3 different treatments (A, B, C). The response for each sample can be reasonably fit with a simple linear ...
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Measuring effects with longitudinal data

Problem: I have sales data through time e.g. how much each user spent on each shopping trip. I am interested in certain events (think users switching to Amazon Prime for instance). I know the date ...